Uncertainty Shocks, Financial Frictions and Business Cycle

Asymmetries Across Countries †

Pratiti Chatterjee‡

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Abstract

This paper explores the interaction of uncertainty shocks and financial frictions in ex-

plaining the excess volatility of real variables in emerging countries vis-a-vis advanced coun-

tries. I use an open economy DSGE model augmented with the financial accelerator mecha-

nism, nominal rigidities and uncertainty evolving as the time-varying volatility of exogenous

shocks. The model is solved using perturbation techniques about a third order approx-

imation to the equilibrium conditions of the model. An uncertainty shock in the model

triggers a precautionary response among agents and generates the simultaneous decline in

GDP, investment and consumption in this open economy environment. Financial frictions

interact with uncertainty to generate the amplified responses in emerging countries along

with producing a strong countercyclical response in trade balances. Using this feature of the

model I estimate key behavioral parameters that guide differences in business cycle charac-

teristics across advanced and emerging countries using a sample of 8 countries (U.S., U.K.,

Canada, France, Mexico, Chile, Argentina and South Korea). The results from estimation

suggest that borrowing costs for non-financial debt in emerging countries are 270-288 basis

points higher compared to advanced countries. While heightened uncertainty is common for

both groups of countries in recessions, differences in financial development captured through

financial frictions is key towards generating the amplified responses in emerging countries.

JEL Classification Codes: C32, E32, F41, E37, F44, G15

Keywords: Uncertainty Shocks, Financial Frictions, Emerging Countries, Recessions, Business Cycles.

†I am grateful to Fabio Milani and Eric Swanson for their extensive guidance and research advice. I amthankful to Gary Richardson, Andrew Foerster and Antonio Rodriguez-Lopez. I want to thank the participantsof 4th Annual Conference of the The Society for Economic Measurement and CAFRAL conference on Financialsystem and Macroeconomy in Emerging Economies organized by the Reserve Bank of India for their feedbackand comments.

‡Contact: Department of Economics, 3151 Social Science Plaza, University of California-Irvine, Irvine, CA92697. e-mail: pratitic@uci.edu.

1

1 Introduction

The emphasis on understanding the role of macroeconomic uncertainty in generating busi-

ness cycle fluctuations has become particularly important in the years following the Great

Recession. Policymakers in various speeches have suggested heightened economic uncertainty

as the chief impediment to the global recovery.1 The other important feature that has garnered

special attention in macro models following the Great Recession is the role of financial frictions.

Prior to the financial crisis the vast majority of the literature assumed frictionless financial mar-

kets.2 The goal of my paper is threefold. First to highlight the importance of the interaction

between financial frictions and aggregate uncertainty in generating recessionary episodes across

different countries (advanced and emerging). Second, to underscore the importance of fragile

financial systems in amplifying a crisis in emerging countries. Third to estimate key parameters

that guide the differences in response across countries.

Specifically, this paper aims to reconcile the differences in the response of real variables to

uncertainty shocks across advanced and emerging countries within the framework of a small

open economy model. I unify the two approaches that traditionally describe the causes of ex-

cess volatility in emerging countries – differences in fundamental features versus differences in

exogenous processes - by examining the interaction of financial frictions and uncertainty shocks.

While contributing to the literature examining business cycle differences across advanced and

emerging countries, this paper also extends the analysis of uncertainty shocks to an open econ-

omy framework.

These two strands of literature – the role of uncertainty shocks in explaining business cycle

fluctuations and the causes of excess volatility in emerging countries - are characterized by

certain stylized facts and modelling conventions. I describe each of these and how I bring

together these different ideas within the framework of this analysis.

The impact of uncertainty on the macroeconomy has been explored in earlier works by

Bernanke (1983) and Dixit and Pindyck (1994). However, the aftermath of the Great Recession

has rekindled the interest in exploring the role of economic uncertainty in generating business

cycle fluctuations with a seminal contribution by Bloom (2009). This strand of literature sug-

gests three main stylized facts that characterize the impact of uncertainty on the macroeconomy.

1Christine Lagarde 2012, Richard W. Fisher 20132DSGE models in the Conduct of Policy: Use as intended, edited by Refet S. Gurkaynak and Cedric Tille

2

First, an increase in uncertainty triggers a ‘wait and see’ response among agents leading to a

simultaneous decline in consumption, investment and output (stylized fact 1). Second, emerg-

ing and low-income countries are more vulnerable to uncertain environments (stylized fact 2).

Third, the effects of higher uncertainty matter more during downturns in the business cycle

(stylized fact 3).

The existing literature has attempted to reconcile the consequences of uncertainty shocks

within the framework of micro founded models. However, the emphasis has largely been fo-

cused towards generating the first stylized fact within the framework of closed economy models

calibrated to match characteristics of developed countries such as the United States (Basu and

Bundick 2017). In the context of international macroeconomics, Fernandez-Villaverde, Guerron-

Quintana, Rubio-Ramırez and Uribe (2011) examine the role of interest rate uncertainty within

the framework of a one sector real business cycle model with the analysis being focused exclu-

sively on emerging countries.

The literature examining the excess volatility of real variables in emerging countries has

evolved along two complementary approaches. On the one hand the work of Aguiar and

Gopinath (2007) emphasizes the differences in exogenous processes as the guiding factor in

the observed excess volatility. The authors show that shocks to the trend of the productivity

process is the main driver of business cycle fluctuations in emerging countries as opposed to

advanced countries which, are characterized by shocks to productivity that are stable about the

trend. The other approach emphasizes that while underlying exogenous processes driving busi-

ness cycles are similar across countries, differences in fundamentals such as weaker institutions,

political instability, and unstable policy amplify the effect of a shock and drive the observed

asymmetry between the two sets of countries.

Among these different channels, financial frictions have garnered special interest. Neumeyer

and Perri (2005) highlight the dependence of country specific characteristics on borrowing costs

within a theoretical framework and subsequently use Argentina as a representative emerging

country to generate the observed excess volatility within this model. Uribe and Yue (2006)

underscore that the feedback from emerging country fundamentals to country spreads signifi-

cantly exacerbate business cycle fluctuations. Fernandez-Villaverde, Guerron-Quintana, Rubio-

Ramırez and Uribe (2011) build upon the results from Uribe and Yue (2006) and explore the

3

uncertainty about interest rates through a stochastic volatility representation for Argentina,

Brazil, Ecuador and Venezuela.

The interaction of financial frictions and uncertainty shocks has been investigated to a cer-

tain extent within closed economy models and empirical studies. Bonciani and Roye (2016),

for instance explore uncertainty shocks in a closed-economy general equilibrium model with a

banking sector and sticky prices. Swallow and Cespedes (2013) examine the impact of uncer-

tainty shocks within an SVAR framework for advanced and emerging countries. One of the

findings from Swallow and Cespedes (2013) paper suggest that, after controlling for credit mar-

ket imperfections such as supply of loans there is a significant reduction in the amplification

of investment for some emerging countries. In the context of international macroeconomics

and business cycle asymmetries across advanced and emerging countries, however, the role of

uncertainty shocks has been investigated to lesser extent.

The novel contribution of this paper is to combine these two approaches in an open econ-

omy model and isolate the role of financial frictions and exogenous shocks to uncertainty in

driving the amplified responses of real variables in emerging countries. I build the theoretical

framework on the empirical findings from Chatterjee (2017) where I document the differences in

the response of macroeconomic variables to uncertainty shocks across advanced and emerging

countries during downturns in business cycles. The findings from Chatterjee (2017) suggest that

uncertainty shocks on average generate an amplified response in emerging countries vis-a-vis

advanced countries in recessions. Furthermore, along the lines of Aguiar and Gopinath (2007),

the results advocate a strong countercyclical response in trade balances to uncertainty shocks

as an important distinguishing feature in the response of real variables to uncertainty shocks

across these two groups of countries. In addition to this asymmetry the findings underscore the

countercyclical nature of uncertainty such that uncertainty shocks are more important during

business cycle downturns and that the linear model consistently underestimates the impact of

uncertainty shocks across countries. These findings are summarized in following figure.

4

Comparing the average effect of a 1% shock to uncertainty across advanced and emerging countries and different modelspecfiications (linear versus nonlinear). The linear model refers to results from a SVAR model. The non-linear modelrefers to the results from the reccessionary regime of the Smooth Transition Vector Auto Regression (STVAR) model. Thelinear model clearly underestimates the effect for advanced and emerging countries alike. Emerging countries, on averageexperience deeper and longer recessions compared to advanced countries, when subject to a 1% shock to uncertainty. Thesample of countries used include the U.S., the U.K., Canada and France as advanced countries and Mexico, Chile, Argentinaand South Korea as emerging countries. The comparison highlights the countercyclical nature of uncertainty shocks andthe need to condition for recessions when evaluating the impact on macroeconomic variables.

In the theoretical specification of my model, following Fernandez-Villaverde, Guerron-Quintana,

Rubio-Ramırez and Uribe (2011), uncertainty stems from the time-varying volatility of exoge-

nous processes (preferences and aggregate productivity). Financial frictions are motivated by

the approach in Neumeyer and Perri (2005) and implemented using the small open economy

version of the financial accelerator of Gertler, Gilchrist and Natalucci (2007). The framework

presented in this paper takes a serious approach in preserving the different aspects of an open

economy model in specifying the dynamics of trade balances and allowing for different degrees

of exchange rate pass-through which is an important empirical distinction between advanced

and emerging countries.

To make uncertainty or shocks to the second moment relevant for the dynamics of the

5

model, I solve the model using perturbation methods, in particular, a third order Taylor Series

expansion as suggested in Andreasen, Fernandez-Villaverde and Rubio-Ramirez (2016). This

deviation from a log-linearized solution also allows for the nonlinear interaction of uncertainty

and macroeconomic variables that is emphasized in the empirical findings from Chatterjee

(2017). Furthermore, a higher order solution allows me to outline the welfare costs of financial

frictions and uncertainty shocks and together with the dynamics enables me to quantify the

role of financial fragility in exacerbating the loss in real activity during periods of heightened

economic uncertainty.

I use a small open economy model with nominal rigidities in prices and foreign currency

denominated debt along with the financial accelerator mechanism. The former ensures a pre-

cautionary response on the part of firms that is key towards generating a simultaneous decline

in investment, consumption and output in response to an uncertainty shock (stylized fact 1

characterizing the impact of uncertainty shocks). The financial accelerator mechanism in con-

junction with foreign currency denominated debt is pivotal in generating the amplified response

in emerging countries (stylized fact 2 – emerging countries are more vulnerable to uncertainty

shocks) along with reproducing stronger countercyclical behavior in trade balances. Finally, I

estimate parameters governing the differences in financial market imperfections and uncertainty

shocks across countries in recessions to shed light on structural differences that exacerbate the

impact of uncertainty in recessions across countries (stylized fact 3 – the impact of uncertainty

shocks is countercyclical in nature). The estimation uses the Impulse Response Function Match-

ing technique and minimizes the distance between the DSGE model implied impulse responses

and the empirical impulse responses. The empirical impulse responses are calculated by using

the recession specific shock to uncertainty from a Smooth Transition Vector Auto Regression

model and generalized impulse responses using the local projection technique from Jorda (2005).

The main results that I present in this paper are threefold. First, the model can generate

the key stylized fact about uncertainty shocks in a small open economy set-up with higher

uncertainty leading to a simultaneous decline in consumption, investment and GDP. Second, I

find that by varying the strength of the financial accelerator mechanism, the model can generate

the amplified responses of real variables (consumption, investment and GDP) with strongly

countercyclical trade balances that is characteristic of business cycles in emerging countries.

6

My findings therefore emphasize the interaction of uncertainty shocks and financial frictions

in generating business cycle asymmetries between advanced and emerging countries. Third,

the results of the estimation suggest that differences in the extent of financial development

captured through financial frictions are key towards generating the differences in business cycle

characteristics for these two groups of countries. I first estimate the model for the U.K and

Mexico – as representatives of advanced-open and emerging-open countries and subsequently

generalize the findings by estimating the parameters by averaging across a sample of 4 advanced

and 4 emerging countries (U.S., U.K., Canada, France, Mexico, Chile, Argentina and South

Korea).

The results from estimation suggest that borrowing costs for non-financial debt in emerging

countries are 270-288 basis points higher compared to advanced countries in recessions. While

heightened uncertainty is common for both groups of countries in recessions, differences in fi-

nancial development captured through financial frictions is key towards generating the amplified

responses in emerging countries. From a policy perspective, the results suggest that investing

in better integrated financial markets and robust financial infrastructure can reduce the volatil-

ity underlying key macro variables in times of high macroeconomic uncertainty for emerging

countries.

The paper is organized as follows. I describe the model set-up in detail in section 2. In section

3, I demonstrate the ability of the model to replicate the first two stylized facts about uncertainty

shocks. First, an upward surge in uncertainty triggers a simultaneous decline in consumption,

investment and GDP in a small open economy model. Second, financial frictions and uncertainty

shocks interact to generate the asymmetric effect of uncertainty shocks across model calibrations

corresponding to representative advanced and emerging countries respectively. In section 4,

I match impulse responses generated from the model with impulse responses to uncertainty

shocks calculated using a combination of parameter estimates from the recessionary regime of

Smooth Transition Vector Auto Regression model and generalized impulse response functions

to estimate the parameters of interest guiding the asymmetry in the behavior of macroeconomic

variables across the two types of countries in recessions. In section 5, I compare the stochastic

and non-stochastic steady states of the model to quantify the loss in real activity attributed to

the interaction of financial frictions and uncertainty.

7

2 Model Specification

This is a model in discrete time where agents live infinitely. There are four agents in this

model economy - households, entrepreneurs, producers of capital goods and retailers. House-

holds consume, supply labor and save in foreign and domestic assets. Entrepreneurs borrow

from global credit markets and use a combination of net worth and foreign currency denomi-

nated debt to raise capital required for the production of wholesale goods. Capital producers

purchase undepreciated capital at the end of each period from entrepreneurs, combine them

with investment to meet the final capital demand from entrepreneurs. Retailers of domestically

produced goods operate within a monopolistically competitive environment. They purchase

wholesale goods from entrepreneurs, costlessly differentiate them and sell the final composite

good to households, capital producers and rest of the world as exports. Retailers of imported

goods also operate within a monopolistically competitive environment and purchase wholesale

goods from rest of the world to costlessly differentiate and sell the final imported good to house-

holds and capital producers. I assume that the main difference between advanced and emerging

countries lies in the cost of credit faced in international capital markets and is specified in the

characterization of the entrepreneurial sector. The behavior of each type of agent is described

in detail as follows:

2.1 Households

Households maximize:

Ut = E0

∞∑t=0

βtzt

((Ct −Ht)

1−ρ

1− ρ− L1+ψ

t

1 + ψ

)

here, Ht denotes the level of habits.3 Lt denotes hours worked. I assume that habits are

external and evolve as function of aggregate consumption in the past, that is, Ht = hCt−1.

Ct is the consumption aggregate across domestic goods CH,t and foreign goods CF,t.1ρ is the

intertemporal elasticity of substitution for habit-adjusted consumption across periods. Presence

3Habit formation in preferences enables the estimation of model parameters. Presence of habits in the utilityof the representative household incorporates the dependence of current consumption on past consumption - thismakes the specification closer to the empirical setup in the Smooth Transition Vector Auto Regression Modelas well as inducing persistence in aggregate consumption. This heps me match the hump shaped response ofconsumption to an uncertainty shock.

8

of external habits will allow for differences in risk aversion (across model specifications for

advanced and emerging countries) for a given value of ρ. β ∈ (0, 1) is the discount factor and zt

is the shock to preferences. The intertemporal shock (zt) governs how consumers weigh current

utility relative to future utility.

There is a unit continuum of differentiated domestic goods and a unit continuum of differen-

tiated foreign goods such that the aggregate consumption basket is defined by a CES aggregator

as follows:

Ct =[(1− γ1)

1η1C

η1−1η1

H,t + γ1η

1 Cη1−1η1

F,t

] η1η1−1

such that

CH,t =[ ∫ 1

0CH,t(i)

ε−1ε di

] εε−1

, CF,t =[ ∫ 1

0CF,t(i)

ε−1ε di

] εε−1

where η1 is the elasticity of substitution between domestic and foreign goods, γ1 is the share

of imports in the consumption basket and ε is the elasticity of substitution across goods within

each category.

The budget constraint faced by the household is given by:

PtCt + PtΓt + bt +XtF∗t = PH,tW

rt Lt + Πt +Rt−1bt−1 +XtR

∗t−1F

∗t−1 (1)

where, the aggregate price index Pt is a CES combination of the price index for domestically

produced goods - PH,t and the import price index PF,t such that:

Pt =[(1− γ1)P 1−η1

H,t + γ1P1−η1

F,t

] 11−η1 such that

PH,t =[ ∫ 1

0PH,t(i)

1−εdi]1−ε

, PF,t =[ ∫ 1

0PF,t(i)

1−εdi]1−ε

W rt is the real wage measured in terms of PH,t that households obtain from supplying labor for

production of wholesale goods. Rt is the gross nominal rate of interest at home and R∗t is the

gross nominal rate of interest abroad. Xt is the nominal exchange rate4. Households can invest

in domestic bonds: bt and foreign bonds: F ∗t subject to portfolio holding costs Γt. The costs to

holding foreign and domestic assets are modeled following Elekdag, Justiniano and Tchakarov

4Home currency price of one unit of foreign currency

9

(2006) and given by:

Γt =φB2

( btPt

)2+φ∗F2

(XtF∗t

Pt

)2

Quadratic costs characterizing portfolio holdings induce stationarity in consumption and stocks

of bond holdings. Households choose Ct, bt, F ∗t , Lt subject to the budget constraint and the

portfolio holding costs. Given, the set-up described above the intra-temporal optimization

condition of the households can be described as follows:

Lψt(Ct − hCt−1

)−ρ =PH,tW

rt

Pt(2)

The Euler equation and the modified uncovered interest parity condition following the optimal

choice for asset holdings imply:

[1 +

φBbtPt

]= βEt

[zt+1

zt

(Ct+1 − hCtCt − hCt−1

)−ρ Rtπt+1

](3)

φBbtPt− φF ∗F

∗t Xt

Pt= βEt

[zt+1

zt

(Ct+1 − hCtCt − hCt−1

)−ρ(Rt/πt+1 −R∗t

Xt+1

Xt/πt+1

)](4)

The optimal allocation of expenditure across home and foreign goods imply the following de-

mand functions for goods produced at home and the foreign country respectively:

CH,t = (1− γ1)( PtPH,t

)η1

Ct

CF,t = γ1

( PtPF,t

)η1

Ct

2.2 Foreign Sector

Aggregate demand (C∗t ), aggregate price index (P ∗F,t) and interest rate (R∗t ) for the foreign

economy (here approximated as rest of the world) are assumed to be constant and treated

as parameters in the model. Following Monacelli (2005) and Gertler, Gilchrist and Natalucci

(2007), I assume that the Law of One Price holds at the wholesale level for foreign transactions.

Price of exports for the home country (imports for rest of the world) evolves as follows:

P ∗H,t =PH,tXt

10

and the demand for exports is given as:

C∗H,t =[γ2

(P ∗H,tP ∗F,t

)−ηC∗t

]ρ′C∗H,t

1−ρ′ (5)

Here, η is the elasticity of substitution between imports and domestically produced goods in the

foreign country. γ2 is the share of imports in the consumption basket of the foreign sector. The

parameter ρ′ helps govern the responsiveness of export demand to changes in domestic prices -

PH,t and Xt by scaling the price elasticity of export demand. ρ′ = 1 implies that a one percent

change in relative prices leads to a change in export demand by η percent, whereas ρ′ ∈ (0, 1)

scales down this effect with the change in demand being given by ρ′η percent.5 Furthermore,

the foreign economy is modeled as a large economy such that imports from the home country

constitute a negligible portion of the consumption basket and P ∗t ≈ P ∗F,t. That is the CPI in the

foreign country is equal to the price of domestically produced goods in the foreign country. I

further set P ∗F,t = 1 while solving the model. This implies that the real exchange rate is defined

as follows:

qt =XtP

∗F,t

Pt=Xt

Pt

2.3 Entrepreneurs

In this paper, I differentiate between advanced and emerging countries in terms of the

cost of credit they face in global credit markets. I empirically validate this assumption by

examining the country-level credit ratings assigned by Standard and Poor across a sample of

82 countries comprising 32 advanced economies and 50 emerging countries. I use credit ratings

as a proxy for the country-specific spread over the risk-free rate (R∗t in this model). As figure

1 demonstrates emerging countries on average receive a rating between BB+ and BBB, in

comparison to advanced countries which receive an average rating between A+ and AA.

5Given that I approximate the foreign sector as rest of the world, ρ′ ∈ (0, 1) enables me to slow down theresponsiveness of exports to changes in domestic prices.

11

Figure 1: Plotting per capita GDP in dollars (x-axis) and country specific credit ratings assignedby Standard and Poor’s for 82 countries - 32 advanced economies and 50 emerging markets (y-axis). Source: International Monetary Fund.

While country specific ratings often account for the differences in the interest rate for

sovereign debt across advanced and emerging countries, there is a very strong co-movement

between corporate and sovereign credit ratings.6 This observed difference in financing debt can

also be attributed in part to country-specific fundamental characteristics such as differences in

the degree of financial integration and intermediation across advanced and emerging countries as

demonstrated by the financial development index in figure 2. The financial development index

is constructed by combining indices measuring financial depth (size and liquidity of markets),

access to financial markets (ability of individuals and companies to access financial services),

and efficiency of financial markets (ability of institutions to provide financial services at low

cost and with sustainable revenues, and the level of activity of capital markets).

6Almeida, Cunha, Ferreira and Restrepo (2014) address this link and demonstrate that the sovereign ratingis the relevant ceiling for ratings on corporate debt.

12

Figure 2: Financial Development Index calculated using the access, depth and efficiency offinancial institutions and markets for advanced and emerging countries. Source: InternationalMonetary Fund.

In order to capture this asymmetry, I model borrowing costs faced by entrepreneurs to evolve

as a function of a global component and a country specific component. The global component

corresponds to the international risk free rate and is constant across countries. The country

specific component is defined to be an increasing function of leverage. I model the higher

borrowing cost faced by emerging countries in international capital markets (as indicated in

figure 1) by making borrowing costs more responsive to leverage for emerging countries. In

order to capture this asymmetry in the responsiveness of borrowing costs to leverage I use

the financial accelerator mechanism outlined in Gertler, Gilchrist and Natalucci (2007) which

generalizes the costly state verification approach adopted in Bernanke, Gertler and Gilchrist

(1999) to a small open economy DSGE model.

Entrepreneurs in this set up are risk neutral and produce wholesale goods by combining the

capital that they own with labor services which they hire from households. Capital required for

production is sourced using a combination of net worth (Nt) and foreign currency denominated

debt (Dt). Debt contracts are defined for one period. To ensure that entrepreneurs continue

to finance capital requirements using a combination of net worth and foreign debt, I assume

that entrepreneurs have a finite life with each surviving the next period with probability θ.

Consequently, the expected lifetime of an entrepreneur is given by 11−θ . Additionally, the

population of entrepreneurs is stationary and exiting entrepreneurs are replaced by new ones.

Each exiting entrepreneur endows the new entrepreneurs with a constant endowment E to ensure

13

that new entrepreneurs have funds to start production. Finally, capital acquired in period t

becomes effective for production in period t+ 1. Entrepreneurs in this framework can thus be

interpreted to represent agents conducting non-financial borrowing. A key assumption that will

guide the dynamics in this model is the role of foreign currency denominated debt.

In each period t, each entrepreneur indexed by net-worth NNt , chooses capital stock (KN

t+1)

to be used for production in period t and labor (LNt ) to be combined with capital from previous

period (KNt ) and used for production of wholesale goods. I start by describing the optimal

choice of labor. Each entrepreneur produces wholesale goods using a Cobb-Douglas production

function where α denotes the share of capital and at is the level of aggregate productivity that

is common to all entrepreneurs such that

Y NH,t = at(K

Nt )α(LNt )1−α (6)

The optimal choice of labor (LNt ) given KNt and at is:

arg maxLNt

PW,tat(KNt )α(LNt )1−α − PH,tWtL

Nt

PW,t denotes the price of wholesale goods. The first order condition with respect to LNt implies:

atPW,tPH,t

(1− α)(KN

t

LNt

)α= W r

t

W rt = Wt

PH,tis the real wage expressed in terms of the domestically produced good. Rewriting

in real terms, by using the domestic price index (PH,t) such that ϕt =PW,tPH,t

:

ϕt(1− α)at

(KNt

LNt

)α= W r

t (7)

Given constant returns to scale in production of wholesale goods and perfectly competitive labor

market, KtLt

=KNt

LNt. The optimal capital-labor ratio is therefore independent of entrepreneur

specific net-worth.

I next proceed to describe the capital acquisition decision. The demand for entrepreneurial

capital depends on the expected return on capital and the expected marginal financing cost.

The expected marginal return on capital in period t is the expected gross revenue net of labor

14

costs normalized by the current market value of capital. The expected gross revenue is the sum

of the expected revenue from selling wholesale goods and sale of undepreciated capital. This

can be summarized as:

EtRK,Nt+1 =

PW,tPH,t

atKNtαLNt

1−α −W rt L

Nt + (1− δ)QtKN

t

Qt−1KNt

EtRK,Nt+1 =

αϕtSH,t

at

(KtLt

)α−1+ (1− δ)Qt

Qt−1

EtRKt+1 =

mpktSH,t

+ (1− δ)QtQt−1

(8)

I next describe conditions that summarize the marginal financial conditions. I restrict my

attention to one period financial contracts that offer lenders a payoff independent of aggregate

risk. I consider a form of the contract that is a reduced form representation of the standard debt

contract with costly bankruptcy as used in Gertler, Gilchrist and Natalucci (2007). The contract

incorporates the possibility of default and subsequently assumes a premium in case of default.

The value of the premium will depend on the country specific fundamental characteristics such

as quality of financial intermediation, extent of financial integration and access to financial

markets as depicted in figure 2. This is analogous to monitoring costs in Bernanke, Gertler and

Gilchrist (1999). I assume that this premium (which is a function of country fundamentals)

varies inversely with the status of development of a country and captures the asymmetry in

borrowing costs demonstrated in figure 1. The debt contract is summarized by the amount

foreign currency denominated loans Dt and interest rate R∗tΨ(t). Here R∗t is the international

risk free rate and Ψ(t) is the country specific component. I model

Ψ(t) = kνt (9)

to be an increasing function of leverage kt = QtKtNt

, and ν is the elasticity of borrowing costs

with respect to leverage. The difference between countries is captured in this model through

different values of ν - such that weaker degree of financial integration (higher monitoring costs)

for emerging countries implies νEmerging > νAdvanced.7 The optimal choice of capital is obtained

7Ordonnez 2010 provides empirical evidence to suggest that monitoring costs or bankruptcy costs are muchhigher in emerging countries vis-a-vis advanced countries

15

by maximizing the ex ante value of entrepreneurial capital V N,et

arg maxKN

t+1V N,et = Et

[RKt+1QtK

Nt+1 −R∗t (kNt )ν

Xt+1

Pt+1DNt+1

]

subject to

QtKt+1 = NNt +

XtDNt

Pt

The first-order conditions of this problem, imply the following marginal financing condition:

EtRKt+1 = R∗t (k

Nt )νEt

qt+1

qtwhere qt =

Xt

Pt

The marginal financing condition captures the external finance premium that arises in equi-

librium. This can be related to the financing premium that arises in Bernanke, Gertler and

Gilchrist (1999) to cover bankruptcy costs. The equilibrium condition also implies that all

entrepreneurs choose the same leverage since from equation 10, kNt can be solved to be indepen-

dent of entrepreneur specific characteristics. Therefore kNt = kt ∀N . The marginal financing

condition can therefore be expressed in terms of aggregate variables:

EtRKt+1 = R∗t (kt)

νEtqt+1

qt(10)

The ex post value of entrepreneurial capital evolves as:

V Nt = RKt QtK

Nt −R∗t kt−1

νqtDNt−1

Integrating of over the mass of entrepreneurs, I obtain the aggregate value of entrepreneurial

capital:

Vt =

∫NV Nt fNdN =

∫N

[RKt QtK

Nt −R∗kt−1

νqtDNt−1

]fNdN =

[RKt Qt

∫NKNt fNdN−

R∗kt−1ν qtqt−1

(Qt

∫NKNt fNdN −

∫NNNt fNdN)

]=

[RKt QtKt −R∗kt−1

ν qtqt−1

(QtKt −Nt)

](11)

where aggregate net-worth Nt =∫N N

Nt fNdN , and aggregate capital stock Kt =

∫N K

Nt fNdN .

16

Finally, given that in each period fraction θ of entrepreneurs survive, aggregate net worth at

the end of each period evolves as:

Nt = θVt + (1− θ)E (12)

where, E is an exogenous constant that ensures that new-born entrepreneurs are endowed with

net-worth to start production.8 An important consideration that I want to highlight at this

point is the balance sheet effect of the real exchange rate. The assumption of foreign currency

debt implies that depreciation of the real exchange rate will dampen the value of entrepreneurial

capital, decrease the net-worth and subsequently increase leverage both through the marginal

financing condition as well as through Vt. Thus, depreciation of the exchange rate in period t

will imply an increase in the external financing premium in period t+1. This effect of exchange

rate on the balance sheet of entrepreneurs is similar to the approach adopted in Cespedes,

Chang and Velasco (2004).

Finally, exiting entrepreneurs consume Cet = (Vt − E) after transferring E to the surviving

entrepreneurs. Consumption is allocated between home goods and imports such that CeH,t =

(1− γ1)(PH,tPt

)−η1

Cet and CeF,t = γ1

(PF,tPt

)−η1

Cet respectively.

2.4 Capital Producers

Capital producers operate in a perfectly competitive environment, purchase undepreciated

capital from entrepreneurs and combine them with new investment goods to construct new

capital that is available for production in the next period. Capital producers use both domestic

and foreign goods for investment such that aggregate investment evolves as follows:

It =[(1− γ1)

1η2 I

η2−1η2

H,t + γ1η21 I

η2−1η2

F,t

] η2η2−1

with:

IH,t =[ ∫ 1

0IH,t(i)

ε−1ε di

] εε−1

, IF,t =[ ∫ 1

0IF,t(i)

ε−1ε di

] εε−1

8This can be endogenized as managerial wages to entrepreneurs as used in Christiano, Motto and Rostagno(2015) which builds off Bernanke, Gertler and Gilchrist (1999). However for the scope of this analysis this variabledoes not play any role. Thus to simplify the model, I assume that E is constant. This parameter helps pin downthe value of transfers along with the exit rate θ that is consistent for a given value of leverage.

17

where η2 is the elasticity of substitution between domestic and foreign goods, γ1 is the share

of imports in aggregate investment and ε is the elasticity of substitution across goods within

each category. The optimal allocation of expenditure across home and foreign goods imply the

following demand functions for goods produced at home and the foreign country respectively:

IH,t = (1− γ1)( PtPH,t

)η2

It, IF,t = γ1

( PtPF,t

)η2

It

The price index for investment is described as a CES combination of the price index for domes-

tically produced goods - PH,t and the import price index PF,t:

P It =[(1− γ1)P 1−η2

H,t + γ1P1−η2

F,t

] 11−η2

where,

PH,t =[ ∫ 1

0PH,t(i)

1−εdi]1−ε

, PF,t =[ ∫ 1

0PF,t(i)

1−εdi]1−ε

Capital production is characterized by adjustment costs following Christiano, Eichenbaum and

Evans (2005) and Smets and Wouters (2007) such that S(.) = S(.)′ = 0 in steady state.

Producers of capital goods choose investment It as follows:

maxIt

Et

∞∑t=0

βtλt+1

λt

[QtKt+1 − (1− δ)QtKt −

P ItPtIt

]

subject to:

Kt+1 = (1− δ)Kt +[1− S

( ItIt−1

)]It

such that S

(ItIt−1

)=τ

2

(ItIt−1

− 1

)2 (13)

This leads to the following optimality condition:

Qt

[1− S(

ItIt−1

)− S′( ItIt−1

)ItIt−1

]+ βEt

λt+1

λtQt+1

[S′(

It+1

It)(It+1

It

)2]=P ItPt

(14)

where λt = (Ct − hCt−1)−ρ

18

2.5 Retailers and the role for nominal rigidities

In the original framework proposed in Bernanke, Gertler and Gilchrist (1999), the role of

retailers is primarily to introduce nominal rigidities in the model so as to analyze the scope

of policy intervention by the central bank. In the present paper, nominal rigidities play an

important role in generating the simultaneous decline in real variables that is characteristic of

an uncertainty shock and is well documented in the empirical literature analyzing uncertainty

shocks. Furthermore, Basu and Bundick (2017) show that nominal rigidities are essential to

guarantee this co-movement in a closed economy model. Additionally, introducing retailers

for imported goods in addition to domestic goods provides flexibility to analyze the responses

of macroeconomic variables under different degrees of exchange rate pass through (Monacelli

(2005)).9

2.5.1 Retailers - Domestic Goods

Following Gertler, Gilchrist, Natalucci (2007) I assume there is a continuum of monopo-

listically competitive retailers of measure unity. Each of these retailers purchases wholesale

goods at price PW,t from the entrepreneurs, differentiates the products slightly and resells the

consolidated aggregate as exports to the rest of the world, to households for consumption and

to capital producers for production of investment goods. Retailers also incur a fixed cost of

production denoted by KH . Fixed costs are chosen such that profits are zero in steady state.

Let YH,t(j) be the output produced by retailer j. Final domestic output is a CES composite of

individual retail goods and is given as:

YH,t =[ ∫ 1

0YH,t(j)

ε−1ε dj

] εε−1 −KH

The assumption CES preferences for households, capital producers and rest of the world implies

that retailer j faces an isoelastic demand given by:(PH,t(j)PH ,t

)−εYH,t. Price stickiness is introduced

a la Calvo with fraction (1− κH) of domestic retailers being able to reset price in each period.

The real marginal cost relevant for retailers of goods produced at home isPW,tPH,t

. The optimal

9The other advantage of introducing nominal rigidities via retailers is to eliminate the loss of output due toprice dispersion. This simplification helps in reducing the number of state variables in the model and aids theestimation by reducing the computational burden.

19

rest price PH,t is given as follows:

PH,t =ε

ε− 1

Et∑∞

s=0(βκH)sΛt+sΛt

ΠεH,t+s

PW,t+sPH,t+s

YH,t+s

Et∑∞

s=0(βκH)sΛt+sΛt

Π1−εH,t+sYH,t+s

where ΠH,t+s =PH,t+sPH,t

with the GDP deflator evolving as:

P 1−εH,t = κHP

1−εH,t−1 + (1− κH)P 1−ε

H,t (15)

2.5.2 Retailers - Imported Goods

For the case of imported goods, I assume incomplete pass through following Monacelli

(2005). Retailers of imported goods purchase imports at dock such that PCP (producer currency

pricing) holds. However, in setting the domestic price of imports the importers solve a dynamic

markup problem characterized by nominal rigidities a la Calvo with fraction 1− κF of retailers

being able to optimally reset the price in each period. The relevant real marginal cost for

retailers of imported goods is thereforeXtP ∗FPF,t

where PF,t is the price of imported goods at home

and P ∗F,t is the foreign currency price of the wholesale imported goods. Similar to retailers of

domestic goods, retailers of imported goods purchase wholesale imported goods, differentiate

them slightly and sell the final consumption aggregate of imported goods to households, and

capital producers. Retailers of imported goods also incur fixed cost of production denoted by

KF . Fixed costs are chosen such that profits are zero in steady state. Let YF,t(j) be the output

produced by retailer j. The final imported good is a CES composite of individual retail goods

and is given as

YF,t =[ ∫ 1

0YF,t(j)

ε1−1ε1 dj

] ε1ε1−1 −KF

CES preferences in households, capital producers and rest of the world implies that retailer j

faces an isoelastic demand given by:(PF,t(j)PF ,t

)−εYF,t. The optimal rest price PF,t is given as

follows:

PF,t =ε

ε− 1

Et∑∞

s=0(βκF )sΛt+sΛt

ΠεF,t+s

XtP ∗F,t+sPF,t+s

YF,t+s

Et∑∞

s=0(βκH)sΛt+sΛt

Π1−εF,t+sYF,t+s

20

where ΠF,t+s =PF,t+sPF,t

with the import price index evolving as:

P 1−εF,t = κFP

1−εF,t−1 + (1− κF )P 1−ε

F,t (16)

The parameter κF controls the degree of exchange rate pass-through in imports in this model

- with values of κF closer to 0 denoting a scenario that is closer to PCP (producer currency

pricing) and values of κF closer to 1 denoting a scenario that is closer to LCP (local currency

pricing).

2.6 Monetary Policy

In this model, household utility is defined in terms of habit adjusted consumption. The

central bank conducts monetary policy taking into account this feature and follows a modified

Taylor rule that responds to CPI inflation (πt), output gap (YH,tYH

) as well as output growth. This

specification of the Taylor rule is similar to what was adopted in Smets and Wouters (2007).

RtR

=

(Rt−1

R

)(1−χ)[(YH,tYH

)χy(πtπ

)χπ]χ( YH,tYH,t−1

)χ∆y

(17)

Here YH is the steady state output and Rt is the gross nominal interest rate and πt = PtPt−1

.

2.7 Market clearing

Market clearing implies the following resource constraint for the model economy:

YH,t =PtPH,t

(Ct + It)︸ ︷︷ ︸Domestic Demand

+ C∗H,t −PF,tPH,t

YF,t︸ ︷︷ ︸Net Exports

+ Cet︸︷︷︸Entrepr. Consumption

+KH +PF,tPH,t

KF︸ ︷︷ ︸Fixed Costs

(18)

Finally, the model is closed by imposing a market clearing condition for domestic bonds. That

is, bt = b.

2.8 Exogenous Processes

The empirical literature examining the effect of uncertainty shocks on macroeconomic vari-

ables typically incorporates a proxy for aggregate uncertainty such that it captures upward

21

surges in uncertainty across different sectors of the economy. Likewise, uncertainty is intro-

duced in the model to reflect this empirical feature.

The model setup described so far, accommodates two sources of exogenous disturbances –

shock to household preferences (zt) entering through the utility function of the representative

household, capturing demand side fluctuations, and shocks to the aggregate productivity process

(at) entering through the Cobb-Douglas production function, capturing supply side fluctuations.

The first moment or the level of aggregate productivity evolves as an AR(1) process given by:

at = (1− ρa)a+ ρaat−1 + σat uat (19)

Likewise, zt evolves as

zt = (1− ρz)z + ρaat−1 + σat uzt (20)

A shock to uat would correspond to a shock to the first moment or a shock to the level of

aggregate productivity while a shock to uzt would correspond to a shock to the first moment

or a shock to the level of the household discount factor β. Given that uncertainty arises in

the model from the time varying volatility of the exogenous disturbances, the key variables

of interest are σat and σzt respectively. σat governs the standard deviation of the aggregate

productivity process while σzt governs the standard deviation of the discount factor associated

with household preferences respectively. I construct σat and σzt to evolve as follows:

σat = (1− ρσa)σa + ρσaσat−1 + ηCu

Ct (21)

σzt = (1− ρσz)σz + ρσzσzt−1 + ηCu

Ct (22)

The definitions of σat and σzt are constructed such that shocks to the standard deviations of zt

and at follow a correlated structure.10 The presence of this common component implies that

a shock to uCt will imply a simultaneous increase in uncertainty about demand as well as the

10The shocks can be constructed such that the specification allows for productivity specific and demand specificuncertainty along with the common component by augmenting equations 20 and 21 as follows:

σat = (1− ρσa)σa + ρσaσat−1 + ηauσa

t + ηCuCt

σzt = (1− ρσz )σz + ρσzσzt−1 + ηzuσz

t + ηCuCt

The results are unchanged if I focus on shock-specific uncertainties i.e. shocks to uσa

t and uσz

t respectively.

22

technology. Therefore, the definition is aligned to the notion of aggregate uncertainty which

typically manifests as uncertainty in all sectors of the economy.11

The important point of distinction between a shock to the first moment (uat , uzt ) and a shock

to the second moment (uCt ) is that for the former, the ergodic distribution of the exogenous

process remains unchanged and only the average level of the exogenous process changes. For an

uncertainty shock however, the average level remains unchanged. Shocks to the second moment

transmit by changing the shape of the distribution and increasing the likelihood of tail events.

These differences in transmission can be observed in figure 3.

Figure 3: Comparing the effects and transmission of shocks to the first and second moment. Ashock to the first moment (uat , u

zt ) does not change the ergodic distribution of the underlying

exogenous process. However, shocks to the second moment (uCt ), alter the distribution of theprocess under consideration and make extreme events more likely than before.

For the rest of the paper uncertainty shocks within the scope of this model will refer to a 1

standard deviation shock to uCt - which has been constructed to represent the theoretical coun-

terpart of aggregate macroeconomic uncertainty. uCt , uat and uzt are iid processes distributed

normally with mean 0 and standard deviation of 1 respectively. The parameters σa(σz), and

ηa(ηz) control the degree of mean volatility and stochastic volatility in aggregate productiv-

ity (preferences): with a high σa(σz) implying a high mean volatility of aggregate productiv-

ity(preferences) and a high ηa(ηz) implying a high degree of stochastic volatility in aggregate

productivity (preferences). Finally, equations 1-22 describe the equilibrium conditions of the

model. I next describe the nonlinear solution technique employed to solve the model.

11Following Basu and Bundick (2017), the shock processes are specified in levels to prevent the volatility of σztand σat from impacting the average values of at and zt through a Jensen’s inequality effect.

23

2.9 Model Solution using numerical techniques

The goal of this paper is to explore the interaction of uncertainty shocks and financial

frictions in generating business cycle asymmetries across countries. While a first order approxi-

mation effectively captures risk aversion, it fails to capture the channels through which precau-

tionary behavior manifests itself in theoretical models. Therefore, following the intuition put

forth in Leland (1968), Sandmo (1970) and Kimball (1990) a precautionary savings response is

motivated by the convexity of the marginal utility function. For firms, the precautionary pricing

channel becomes relevant when their decisions explicitly incorporate the changes in the standard

deviation of exogenous processes that govern final demand. To incorporate these dimensions in

the solution of the model, it is important to deviate from a first order approximation.

A second order solution is not sufficient to generate dynamic effects to an uncertainty shock

since the coefficients on the linear and quadratic terms for the state vector for a second-order

expansion of the decision rule are independent of the volatility of the exogenous shocks (Schmidt-

Grohe and Uribe 2004). Therefore, if I consider a second order solution, uncertainty will impact

the steady state of the model however, will not impact the dynamics.

To ensure that uncertainty or properties of second moments impact the dynamics of the

model, I need to consider at least a third order approximation. To achieve this, I use perturba-

tion techniques suggested in Andreasen, Fernandez-Villaverde and Rubio-Ramirez (2016). The

solution technique uses pruning to generate closed form solutions for impulse responses, as well

as the first and second moments for the endogenous variables.

Furthermore, using a third order solution provides me the flexibility to compare the non-

stochastic steady state and the stochastic steady state of the model to isolate how fundamental

differences such as fragile financial markets can influence the dynamics of the model. The

impulse responses uses this stochastic steady state as an input and is computed as the difference

between the conditional (conditioning on the uncertainty shock being different from zero) and

unconditional expected values (stochastic steady state of the model).

The research questions that I seek to answer through this paper are threefold. First, the

standard new Keynesian DSGE model augmented with financial frictions and uncertainty shocks

can generate the stylized facts that characterize the response of uncertainty across advanced

and emerging countries alike. Second, fragile financial markets in emerging countries captured

24

in the model through higher values of ν -elasticity of borrowing costs with respect to leverage

in conjunction with foreign currency denominated debt generates the amplified response in

emerging countries vis-a-vis advanced countries. Third, use the qualitative features of the

model to estimate key parameters that differentiate the response to uncertainty shocks across

advanced and emerging countries.

The calibration exercise describe the in next section, aims to have a model parameterization

that enables me to demonstrate the qualitative features of the model and shedding light on how

an uncertainty shock transmits in the model. After establishing these features, I proceed to the

estimation in section 4.

2.10 Model Calibration

Calibrating external finance premium across countries: In order to emphasize the

interaction of borrowing costs and aggregate macroeconomic uncertainty in generating the ex-

cess volatility in emerging countries vis-a-vis advanced countries, I calibrate the representative

models for advanced and emerging countries to differ only on the dimension that governs the

spread over the international risk free rate. This is captured by the parameter ν in the model.

I calibrate the parameters such that the leverage is same however the parameter ν is differ-

ent. The model is then able to capture the differences in the transmission of an uncertainty

shock that is entirely attributed to the cost of credit for calibrations representing advanced and

emerging countries respectively. The steady states of the model calibrated for the same level of

leverage but different ν reflects how higher borrowing costs translates into lower values of GDP,

consumption and investment. I present these details when I discuss the welfare implications in

section 5. Table 1 defines the calibrations for representative advanced and emerging countries.

The given values of leverage and ν imply borrowing costs of 4.76% and 7.68% per quarter for

Model type Leverage(k)

Elasticity of borrowing costs wrtleverage (ν)

Representative Advanced Country 2.5 0.04Representative Emerging Country 2.5 0.07

Table 1: Calibrating ν

the representative emerging and advanced country respectively.

Calibration strategy for exogenous processes: The volatility of stock market return is a

25

commonly used empirical proxy for measuring aggregate macroeconomic uncertainty. I use this

to calibrate the mean volatility of productivity (preferences) across - σa(σz) model calibrations.

The average volatility of stock market returns between 1993Q1 − 2014Q4 is 0.112 for Mexico

(representative emerging country) and 0.076 for the United Kingdom (representative advanced

country). In order to isolate the role of borrowing costs and demonstrate the effectiveness of the

model in capturing the asymmetric effect of uncertainty shocks across representative advanced

and emerging countries, I fix the mean volatilities to 0.112 across calibrations (details in table

2) for advanced and emerging countries. However, in section 4 when I estimate the recession

specific estimates of borrowing costs, I allow this parameter to vary across countries. The

parameter ηC which capture the extent of stochastic volatility is calibrated such that a one

standard deviation shock in the model corresponds to a 1% increase in the standard deviation

of productivity (and preferences). The AR(1) coefficients are calibrated such that shocks to

uncertainty are moderately persistent in the model - this is reflecting the empirical feature that

upward surges of uncertainty are relatively short lived. Like the average level of uncertainty, I

estimate the parameters governing the persistence of the shocks in section 4.

Parameter Definition Calibrated Valuesσa = σz Mean Volatility 0.112ηC Stochastic Volatility 0.00112ρσa Persistence: σat 0.83ρσz Persistence: σzt 0.85ρa Persistence: at 0.75ρz Persistence: zt 0.85a = z Mean: Level 1

Table 2: Calibrating uncertainty shocks

The remaining behavioral parameters have been calibrated as follows:

Households: I fix the discount factor β to 0.997, the coefficient of risk aversion ρ = 2.

Household consumption is characterized by external habits with the parameter h governing

the extent of indexation to past consumption. For the first set of results where I compare the

strength of the model in generating business cycle asymmetries for calibrations corresponding to

representative advanced and emerging countries I set h = 0.5. However, in section 4, I estimate

the value of this parameter. The calibrated values for h and ρ imply an intertemporal elasticity

of substitution of 0.25.12 The Frisch elasticity of substitution is obtained as 1ψ = 0.5 by setting

12The formula for the intertemporal elasticity of substitution being given as 1ρ/1−h .

26

ψ = 2.13 The elasticity of substitution between exports and imports for consumption - η1 is set

to 0.89 (following Gertler, Gilchrist and Natalucci (2007))14. η - the elasticity of substitution

between exports and imports for the foreign sector is set to 1 allowing for a greater degree of

substitutability for rest of the world relative to the small open economy under consideration.

Portfolio holding costs for domestic (φB) and foreign assets (φF ) are set to 0.0009 and 0.009

respectively. The portfolio holding costs in conjunction with the discount factor, and steady

state level of domestic bond holdings pin down the steady state value of the domestic interest

rate.

Entrepreneurs: In addition to leverage (k) and elasticity of borrowing costs with respect

to leverage (ν), the other parameters that characterize the choices of the entrepreneurs are - α

- share of capital in the production function and θ - the exit rate of entrepreneurs. I fix α to 0.5

(following Gertler, Gilchrist and Natalucci (2007)). I set θ to 0.915 as estimated by Fernandez

and Gulan (2015) for the calibration corresponding to a representative emerging country. To

preserve symmetry in all dimension excepting ν I calibrate θ to 0.915 for the representative

advanced country as well.

Retailers: In addition to leverage and the elasticity of borrowing costs with respect to

leverage , the other parameter that is important in driving the results is the extent of nominal

rigidities. I calibrate κH = 0.75 - implying an average duration of 11−κH = 4 quarters for

prices set by domestic retailers. The parameter κF governs the extent of price stickiness for

firms selling imported goods. This parameter can also capture the extent of exchange rate pass

through given the model specification. Higher values of κF imply a lower extent of exchange rate

pass through. I calibrate κF = 0.25 to demonstrate the initial set of results however, in section

4, I estimate this parameter. The elasticity of substitution across goods within a category

(domestically produced and imports) is set to 8 such that in steady state firms experience a

mark-up of ≈ 15%.

Capital Producers: The key parameters of interest for capital producers comprise the

elasticity of substitution between domestic goods and imports for investment goods - η2, the

depreciation rate of capital- δ and investment adjustment costs S′′(.). For simplicity I set η2 =

13Decreasing the elasticity of labor supply amplifies the impact of uncertainty shocks.14Decreasing the elasticity of substitution between exports and imports for the foreign sector amplifies the

impact of uncertainty shocks.

27

η1 = 0.89 - the elasticity of substitution between domestic goods and imports for consumption.15

δ is calibrated to 0.05. S′′(.) is calibrated to 6.

Monetary Policy: The parameters of the Taylor rule are set to standard values adopted

in the literature with the coefficient on inflation χπ = 1.5, coefficient on output gap with respect

to steady state χy = 0.08 and coefficient on the growth rate of output χ∆y = 0.22

Table 3: Calibration

Parameter Definition Calibrated Value

Households1

ρ/(1−h)Intertemporal Elasticity of substitution (after adjustingfor habits)

0.25

h Habit 0.5ψ Frisch elasticity of labor supply 2η1 Elasticity of substitution between

home and foreign goods for consumption0.89Gertler, Gilchrist and Natalucci (2007)

φB , φ∗F Portfolio Holding Costs 0.00009, 0.0009β Discount Factor 0.997γ1 Share of home goods in aggregate consumption 0.55

Foreign Sector

η Elasticity of substitution betweenhome and foreign goods for foreign country

1Gertler, Gilchrist and Natalucci (2007)

γ2 Share of goods produced at home -exports for rest of theworld

0.0187

C∗ Aggregate consumption for rest of the world 200P ∗F CPI for Rest of the world 1R∗ Gross foreign Interest Rate (quarterly) 1.0099 (1.04% Annualized after quarterly

compounding)1− ρ′ Persistence of export demand from rest of the world 0.75

Entrepreneurs

α Share of capital in production process 0.5, Gertler, Gilchrist and Natalucci (2007)θ Exit rate of entrepreneurs 0.915, Fernandez and Gulan (2015) estimate

0.9

Capital Producers

η2 Elasticity of substitution betweenhome and foreign goods for investment

0.89

δ Depreciation rate 0.05S′′ Elasticity of investment adjustment costs 6 Smets and Wouters (2007) use 5.74

Retailers

ε Elasticity of substitution across varietiesfor domestically produced goods

8

ε1 Elasticity of substitution across varietiesfor foreign goods

8

κH Calvo price stickiness for retailers of domestic goods 0.75 Gertler, Gilchrist and Natalucci (2007)κF Calvo price stickiness for retailers of imported goods 0.25

Monetary Policy: Taylor Rule Coefficients

χy Output deviation from steady state 0.08 - Smets and Wouters (2007)χ∆y Output growth 0.22 Smets and Wouters (2007)χπ CPI inflation 1.5

15Typically, investment goods exhibit a lower degree of substitution in comparison to consumption goods.Letting the price indices for investment and consumption to display this heterogeneity will amplify the effects ofuncertainty shocks.

28

Finally, while solving the model I assume that Cet is set equal to zero. This is aligned to the

assumption in Bernanke, Gertler and Gilchrist (1999) which fixes the share of entrepreneurial

consumption to 0.01. This simplification does not alter the dynamics of the model.

3 Transmission Mechanism of an Uncertainty Shock

Uncertainty shocks in a stochastic volatility environment arise from shocks to the standard

deviation of exogenous processes. In this model, uncertainty shocks are therefore captured by

shocks to uCt . The correlated structure between the standard deviations of aggregate produc-

tivity (at) and the exogenous component of the discount factor (zt) will imply that a shock to

uCt will translate into an increase in uncertainty about productivity as well intertemporal dis-

counting by households. Given that the solution is computed using a third order approximation

of the equilibrium conditions, this increase in uncertainty about productivity and the discount

factor will simultaneously trigger a precautionary response among households and firms. Thus,

even though, an uncertainty shock will have no first order properties, through the third order

precautionary channel, it will generate a first order change in real activity.

For the scope of demonstrating the transmission mechanism I focus on a one standard

deviation shock to uCt . The model calibration is such that a one standard deviation shock to

this common component leads to 1% increase in the volatility of preferences and aggregate

productivity respectively.

An increase in uncertainty in the model - implies a mean preserving spread for aggregate

productivity (at) and the exogenous component of the discount factor (zt). This change in the

shape of the distribution of the exogenous processes implies that tail events are more likely than

before. This is key towards generating a precautionary response among agents in the model

economy.

Given, that a bad outcome for productivity is more now likely firms engage in precautionary

pricing behavior to hedge against risks of reduced profitability in the future by increasing

their mark-up over marginal cost (similar to the approach in Born and Pfeifer 2017). This

consequently leads to an inward shift of the labor demand curve. The increased mark-up

translates to an increase in the price of domestic goods triggering a decrease in consumption

and investment demand along with an increase in the marginal utility of wealth.

29

The decrease in consumption demand is amplified as households respond to uncertainty

about future preferences by engaging in precautionary savings behavior – reducing consumption

demand and increasing labor supply. This leads to an outward shift of the labor supply curve.

In equilibrium, wages and hours both decline on impact. The dynamics of labor demand relies

crucially on nominal rigidities for retailers of domestic goods and emphasizes the mechanism

suggested in Basu and Bundick (2017). Figure 4 illustrates these dynamics.

Figure 4: Solid line: Advanced Country, Dashed line: Emerging Country. Precautionary pricingby firms and precautionary savings by households with nominal rigidities leads to a decrease inwages and hours supplied.

The reduction in investment demand triggered by the increase in mark-up leads to a decline

in the price of capital. Given that both the level of capital stock and the level of aggregate

productivity remains unchanged, the fall in employment triggers a decline in the marginal

productivity of capital. This in conjunction with the decline in the price of capital causes

the real rate of return on capital to fall. This decline in the rate of return on capital erodes

30

entrepreneurial net-worth and causes leverage to increase. This is can be seen by examining

the expression for the entrepreneurial value of capital (Vt), net-worth (Nt) and leverage (kt)

respectively:

Vt =

[RKt QtKt −R∗kt−1

ν qtqt−1

(kt − 1)Nt

], kt =

QtKt

Nt, Nt = θVt + (1− θ)E

These dynamics are qualitatively similar across the two calibrations of the model with the

calibration corresponding to emerging countries exhibiting an amplified response. (Refer to

figures 4 and 5)

Figure 5: Solid line: Advanced Country, Dashed line: Emerging Country. Simultaneous declineof capital prices and the marginal productivity of capital reduces the rate of return on capitaland erodes entrepreneurial value of capital along with increase in leverage

The main differentiating feature in responses is brought about by the equilibrium condition

31

that defines the marginal financing condition. Recall,

EtrKt+1 = R∗t

[QtKt

Nt

]ν qt+1

qt

When the value of ν is large enough, the decrease in capital demand triggered by the de-

crease in investment is not sufficient towards restoring equilibrium by countering the effect of

an increase in leverage. This initial increase in leverage is brought about by the decrease in the

value of entrepreneurial capital. Therefore, to restore equilibrium, the currency depreciates and

qt increases. The depreciation of domestic currency further erodes the value of entrepreneurial

capital and increases leverage. Thus, for νEmerging > νAdvanced, the initial amplification in lever-

age induced by a higher value of ν is further amplified due to the depreciation of the exchange

rate. Higher elasticity of borrowing costs with respect to leverage in conjunction with foreign

currency denominated debt are key channels that generate the amplified responses in lever-

age, exchange rate and investment for the calibration corresponding to that of a representative

emerging country.

In addition to reinforcing the financial accelerator mechanism, if the depreciation in the real

exchange rate offsets the increase in the price of domestic goods (PH,t) relative to the CPI (Pt),

it triggers an increase in the demand for exports from rest of the world. This is can be seen

from the following equation governing export demand:

C∗H,t = [γ2

(P ∗H,tP ∗F,t

)−ηC∗t ]ρ?C∗H,t

1−ρ?

= [γ2

( PH,t/PtXtP ∗F,t/Pt

)−ηC∗t ]ρ′C∗H,t

1−ρ′

= [γ2

(qt

PtPH,t

)ηC∗t ]ρ?C∗H,t

1−ρ′

with qt =Xt

Ptand P ∗F,t = 1

Therefore as long as the increase in qt exceeds the decline in PtPH,t

, demand for exports increases

in response to an upward surge in aggregate uncertainty. These dynamics are demonstrated in

figure 6.

While on the one hand a weaker domestic currency propels export demand, on the other

hand, it amplifies the decline in import demand. Thus, in conjunction, the two can generate an

32

increase in net-exports. For the calibration corresponding to a representative advanced country,

this depreciation of the real exchange rate is absent. Consequently, the calibration does not

generate this countercyclical response in trade balances. The model calibrations differing only

with respect to this one parameter ν is not only able to generate the asymmetric response in real

variables to uncertainty shocks, with larger values of ν leading to an amplified decline. It is also

able to generate the strong countercyclicality in trade balances that is the key distinguishing

feature between business cycles in advanced and emerging countries.

Figure 6: Solid line: Advanced Country, Dashed line: Emerging Country. Divergence in theresponse of the real exchange rate across calibrations for advanced and emerging countries isinduced by differences in higher borrowing costs in emerging countries

Finally, given that the decline in consumption and investment demand exceed the increase

in net-exports, overall GDP declines. The model specification can successfully generate the

simultaneous decline in consumption, investment, and GDP along with a strong countercyclical

response by trade balances for the model calibration corresponding to an emerging country.

Furthermore, the model can produce the asymmetry in the responses of real variables to an

uncertainty shock across model calibrations for advanced and emerging countries. The dynamics

of GDP, investment and consumption can be seen in figure 7.

The main takeaway from the transmission mechanism is: even though an increase in un-

certainty might not lead to a negative outcome ex post, precautionary actions by agents can

generate decline in real activity that is of first order importance. Furthermore, for countries

that are financially fragile this precautionary response is amplified - generating deeper and a

33

more persistent decline in real activity along with a strong countercyclical response in trade

balances.

Figure 7: Solid line: Advanced Country, Dashed line: Emerging Country. Simultaneous declinein investment, consumption and GDP in response to an uncertainty shock.

The goal of the calibration exercise was to demonstrate that the model can generate the

features that characterize the impact of uncertainty in the model economy. Now that I have

successfully reproduced these qualitative features, I proceed to estimating the key parameters

guiding the differences in response across advanced and emerging countries.

34

4 Estimating the role of financial frictions across countries in

recessions

The results so far underscore the interaction of uncertainty shocks and financial frictions

in generating business cycle asymmetries across advanced and emerging countries. Empirical

evidence16 on the impact of uncertainty shocks on real variables suggest that the effects of

macroeconomic uncertainty are largely countercyclical. That is, upward surges in macroeco-

nomic uncertainty matter more during downturns in business cycles.

To test this interaction between financial frictions and uncertainty shocks in recessions I

use a modified version of the VAR-based impulse response function matching estimator. I

estimate the role of financial frictions and uncertainty shocks in recessions by using a two-step

procedure in a limited information environment. First, I estimate a Smooth Transition Vector

Auto Regression Model (STVAR) to obtain recession specific coefficients and a recession specific

measure of an uncertainty shock. Next, I use this recession specific shock to compute generalized

impulse responses using the technique of local projections as outlined in Jorda (2005).

4.1 Calculating recession specific impulse responses

Using a combination of the STVAR model and the technique of local projection mapping

from Jorda (2005), I first estimate the behavioral parameters for the U.K and Mexico to compare

the differences in parameters pivotal for the asymmetric transmission of uncertainty between

advanced and emerging countries. The reason for this choice is the availability of substan-

tial data with sufficient recessionary episodes17. This allows me to estimate a more detailed

specification for these countries.

The choice of the U.K and Mexico as representative advanced and emerging countries

is also justified as both countries exhibit a comparable degree of openness to trade,18 both

countries follow similar monetary policy (with emphasis on inflation targeting) and this al-

lows me compare the impact of uncertainty after conditioning for the role of policy and de-

gree of openness. For these two countries, the model is estimated using a specification with

Yt = [Ut, It, Ct, TBt,Πt, rt]′ where U is the country specific proxy for ‘aggregate macroeconomic

16Jurado et al 2015), Bloom (2015), Caggiano, Castelbuovo, and Groshenny (2014)17I discuss data limitations and constraints in detail in Chatterjee 201718≈ 52% for the U.K between 1979 Q1 and 2014 Q2 and for Mexico between 1993 Q1 and 2014Q2

35

uncertainty’, I is the growth rate of investment, C is the growth rate of consumption, TB is

the first difference of net exports expressed as a percentage of GDP, Π is the inflation and r is

the policy rate. To generalize the findings from the estimation exercise, I extend the sample

of advanced countries to the U.S., France, Canada, and emerging to South Korea, Chile and

Argentina. I estimate the STVAR with fewer variables - Yt = [Ut, It, Ct, TBt]′19 to overcome

the data constraints for this expanded sample, compute the average impulse responses to un-

certainty across the 4 advanced and 4 emerging countries, and subsequently estimate the key

behavioral parameters that characterize the differences in the impact of uncertainty for these

two country groups on average.

I now describe the STVAR model is detail. The STVAR model distinguishes between a

recessionary regime and a ‘catch all’ non-recessionary regime. The model also, incorporates the

ability to allow for country specific differences in guiding the smoothness of transition across

regimes. The detailed model specification is given below:

Yt = F (zt−1)BR(L)Yt + (1− F (zt−1))BNR(L)Yt + εt (23)

εt ∼ N(0,Ωt) (24)

Ωt = F (zt−1)ΩR + (1− F (zt−1))ΩNR (25)

F (zt) =exp(−γzt)

1 + exp(−γzt)and γ > 0 (26)

E(zt) = 0 and V ar(zt) = 1 (27)

Yt = [Ut, It, Ct, TBt,Πt, rt]′ or Yt = [Ut, It, Ct, TBt]

′ depending on the choice of country and

data availability. I quantify uncertainty by using the volatility of stock market returns. I have

constructed the quarterly measure of country specific uncertainty by averaging the monthly

standard deviation of stock market returns calculated using daily data. Volatility of stock

19For the U.S. the model is estimated using Yt = [Ut, It, Ct, TBt,Πt, rt]′

36

market returns is standard measure of macro-financial uncertainty, however, Bloom (2014)

demonstrates that measures such as the VIX, standard deviation of stock market returns are

correlated with other measures of macroeconomic uncertainty and can be used to represent

aggregate macroeconomic uncertainty as well.

The remaining endogenous variables included in the system are investment - It (gross fixed

capital formation), consumption - Ct (private consumption expenditure), trade balances - TBt

(net exports of goods and services expressed as a percent of GDP), inflation - Πt (quarter on

quarter change in the GDP deflator) and interest rate rt (policy rate or closest available proxy).

Investment and consumption are in log first differences. For trade balances the first difference

in the ratio of net exports to GDP has been taken. I use data that has been seasonally adjusted.

Data sources and variable definitions have been provided in detail in tables 2 and 3 - section 3

of the appendix.

As described in the model specification, the STVAR framework allows for a two-way prop-

agation mechanism for shocks to uncertainty. The regime specific VAR coefficients defined by

BR, BNR allow for dynamic propagation of shocks and the regime specific variance covariance

matrices ΩR, ΩNR allow for contemporaneous propagation of uncertainty shocks. BR, ΩR,

therefore, describes the behavior of the economy deep in recessions and likewise, BNR, ΩNR

describes the behavior of the economy during ‘catch all’ non-recessionary phases.

The parameter γ > 0 governs the smoothness of transition from recessionary to the non-

recessionary regime. As γ → ∞ the transition becomes very abrupt between the regimes,

whereas setting γ = 0 reverts the system to the linear VAR specification. I set γ = 1.75 for the

U.K and γ = 2.5 for Mexico to capture the differences in volatilities exhibited by key macro

variables across the two countries. Table 1 in the appendix lists the parametrization of γ for the

entire sample. The variable zt governs the transition from one regime to the other. The goal is

to capture the differences in business cycles across countries by appropriately calibrating γ and

choosing the state transition variable such that the system spends sufficient time in recessions.

In the current set up F(z) is given by the logistic function. It defines the likelihood of being in

any particular state, with F(z) ≈ 1 implying the recessionary regime and F(z) ≈ 0 implying the

expansionary regime. The logistic function is used for assigning regime specific probabilities by

using the smoothness parameter (γ) and the state transition variable (zt) as inputs.

37

Following Auerbach and Gorodnichenko (2012) the transition function enters the VAR spec-

ification (equation 23) with a lag of one period to avoid contemporaneous effects of policy vari-

ables in defining the state of the economy. The state transition variable is not included in

the system of endogenous variables, thus, eliminating interaction and feedback effects between

the state transition variable and the dynamics of the macroeconomic variables included in the

system. The choice of the transition function is very important as this is the driving force that

induces non-linearities in endogenous variables at turning points in the business cycle. While

there are multiple ways to capture regime switches in the business cycle, following Auerbach

and Gorodnichenko (2012) (and what was adopted in Caggiano, Castelnuovo and Groshenny

2014), I have defined zt to be the standardized 7 quarter moving average of the growth rate of

real GDP. Therefore, zt > 0 implies that the growth trajectory of real GDP is above average

and vice versa.20

Using the recession specific variance-covariance matrix ΩR, and Cholesky identification, I

construct the uncertainty shock that is subsequently used to compute the generalized impulse

responses). This non-parametric method of calculating impulse responses, benefits the estima-

tion in two ways. The STVAR model does not include zt or the state transition variable in

the model specification and in process eliminates feedback arising from an uncertainty shock

to the definition of a recession. The impulse responses obtained using a combination of reces-

sion specific coefficients BR and recession specific shock ΩR ignores the possibility of regime

changes during the propagation. The use of GIRFs allows me to bypass this assumption of

conditional linearity in calculating impulse responses and accommodate for the possibility of

regime switches during the transmission process. Second, this allows a one for one comparison

between the theoretical and empirical impulse responses. However, as a robustness check, I also

estimate the parameters using the conditionally linear recession specific impulse responses to

find qualitatively similar estimates across both measures.

4.2 Impulse Response Function Matching Estimator (IRFME)

The impact of an uncertainty shock on macroeconomic variables is typically characterized

by the simultaneous decline in consumption, investment and GDP. Therefore, while estimat-

ing the role of financial frictions in generating business cycle asymmetries across countries,

20Using a standardized estimate of zt helps in eliminating scale dependence of zt.

38

I attempt to match the responses of consumption and investment. I exclude GDP from the

STVAR since, the seven quarter moving average of real GDP growth rate is used as an input

in defining the regime specific probabilities. Including, real GDP as a variable in the STVAR

specification while estimation, would imply that the regime changes maybe induced by changes

in uncertainty. While this is an interesting question in itself, the main point of focus in this

section is to isolate the impact of upward surges in uncertainty during recessionary episodes and

quantify the strength of the financial frictions channel in generating the heterogeneous response

to uncertainty shocks across countries. As highlighted earlier, I incorporate the possibility of

regime switches during the propagation by calculating the generalized impulse responses using

the recession specific shock identified from the STVAR model using the same variables that are

used as inputs for estimating the STVAR model.

Finally, a comment on the ordering of variables - the impulse responses to a 1% shock to

uncertainty have been constructed with uncertainty ordered as the first variable in the STVAR.

This means that the one step ahead forecast error in ‘country specific uncertainty’ is attributed

in entirety to uncertainty shocks. This ordering matches the formulation in the theoretical

model described in section 3, where uncertainty is interpreted as the time varying volatility of

the process governing the evolution of aggregate productivity and preferences. The approach

is similar to what has been adopted in Basu and Bundick (2017) where an upward surge in

uncertainty is causally prior to the responses of macroeconomic variables. Furthermore, Basu

and Budick (2017) demonstrate that the theoretical counterpart of the VIX in their model is

relatively unresponsive to non-uncertainty shocks.

I proceed to defining the Impulse Response Function Matching Estimator (IRFME) following

Hall, Inoue, Nason and Rossi (2012) that helps isolate the role of key behavioral parameters that

guide the differences in transmission across countries. This technique has been used extensively

in other papers such as Christiano, Eichenbaum and Evans (2005) and Christiano, Eichenbaum

and Trambandt (2015).

Let, γ denote impulse responses generated from the DSGE model such that,

γ = g(φ, φ, h)

Let n denote the total number of parameters in the model and φ = [φ1, .., φn1 ] denote the

39

subset n1 < n parameters that I estimate using the IRFME procedure. φ = [φn1+1, .., φn]

denotes the set of calibrated parameters in the model. Let γ denote the impulse responses to

a 1% uncertainty shock constructed by identifying the shock corresponding to the recessionary

regime of the STVAR model and implemented using the generalized impulsed responses. γ

therefore corresponds to the estimate of γ. The IRFME of φi= φi(φ, h) ∀i ∈ 1, .., n1 such that:

φ1(φ, h)

φ2(φ, h)

...

φn1(φ, h)

= arg min

φ1(φ,h),..,φn1 (φ,h)

[γ − g(φ, φ, h)]′ΩT (h)[γ − g(φ, φ, h)]

The goal of the estimation procedure is to emphasize the differences in key behavioral param-

eters that guide the differences in the response of macro variables to uncertainty shocks across

countries. The main ingredients that characterize this difference are the elasticity of borrowing

costs with respect to leverage - ν, the average level of uncertainty in the economy σa and σz,

the persistence of second-moment shocks to productivity (and preferences) ρσa (and ρσz), the

degree of exchange rate pass-through κF , the persistence of external habits - h and the elasticity

of labor supply ψ. While estimating the parameters, I hold the leverage fixed across countries

to 2.5 so that the parameter ν can entirely capture country specific differences in borrowing

costs. Finally, I set ΩT = I such that both consumption and investment are assigned equal

importance during the optimization routine.

4.3 Results of the IRFME procedure

The results suggest substantial differences in borrowing costs faced by these two countries

at a quarterly level with Mexico facing interest rates that are 288 basis points higher in com-

parison to the United Kingdom. The average level of uncertainty is higher for both countries for

shocks that originate in recessions with the U.K recording higher average uncertainty (about

8.5%). These results suggest financial fragility is more important in comparison to the ex-

ogenous shock in generating the excess volatility of real variables in a representative emerging

country like Mexico. An important thing to note is that while the qualitative features of the

transmission mechanism are governed exclusively by ν, the quantitative features are governed

40

Parameter Mexico United Kingdom

ν - Elasticity of borrowing costs wrt leverage 0.0713 0.0418σa = σz - Average uncertainty 0.2456 0.2685ρσz - - Persistence of second-moment shock - preference 0.949 0.9078ρσa - Persistence of second-moment shock -productivity 0.8622 0.854h - Persistence of external habits 0.4701 0.5031κF - Degree of exchange rate pass through - extent ofnominal rigidities in imports

0.2481 0.4996

ψ - Frisch elasticity of labor supply 2.0121 3.0026Est. RKt+1 1.0781 1.0493

Table 4: Estimating behavioral parameters guiding the differences in the transmission of uncer-tainty shocks for Mexico and the United Kingdom

by the interaction of ν as well as the higher level of uncertainty. The persistence parameters

of second moment shocks suggest that an uncertainty shock that originates during a recession

lasts longer in an emerging country like Mexico. The higher degree of price stickiness in imports

in the United Kingdom are aligned to findings from Gopinath (2012) which suggests advanced

countries are closer to a ‘local currency pricing (LCP)’ model for imports. While estimates

for κF in Mexico suggests evidence leaning towards a ‘producer currency pricing (PCP)’ in

imports. In figures 8 and 9, I compare the empirical IRFs with those generated from the model

and calculated using parameters reported in table 4.

Figure 8: Comparing impulse responses to a 1% uncertainty shock generated from the STVARmodel (solid line) and theoretical model (dashed line) for Mexico

41

Figure 9: Comparing impulse responses to a 1% uncertainty shock generated from the STVARmodel (solid line) and theoretical model (dashed line) for the United Kingdom

To generalize the findings from the estimation, I expand the sample of advanced countries to

include the U.S., France and Canada along with the U.K. and the sample of emerging countries

to include Chile, Argentina and South Korea along with Mexico. Using a combination of

the STVAR model and the GIRFs I construct country specific impulse responses to a 1%

uncertainty shock and then average across these two 4-country groups to construct the average

effect of uncertainty shocks across advanced and emerging countries. The estimation technique

is exactly the same as described earlier.

Parameter Average -EmergingMarkets

Average -AdvancedEconomies

ν - Elasticity of borrowing costs wrt leverage 0.0687 0.0408σa = σz - Average uncertainty 0.3 0.2891ρσz - Persistence of second-moment shock - preference 0.8 0.82ρσa - Persistence of second-moment shock -productivity 0.824 0.8199h - Persistence of external habits 0.4374 0.5031κF - Extent of nominal rigidities in imports 0.2427 0.5002ψ - Inverse of Frisch elasticity of labor supply 5.007 4.0039Est. RKt+1 1.0756 1.0484

Table 5: Estimating behavioral parameters guiding the differences in the transmission of uncer-tainty shocks for representative advanced and emerging countries

As before, differences in the parameter governing the elasticity of borrowing costs wrt lever-

age leads to borrowing costs that significantly higher in emerging countries with the difference

amounting to 270 basis points. The average level of uncertainty is relatively as before is

comparable across the country groups with emerging countries on average recording higher un-

42

certainty. The findings with the broader group of countries reinforce the initial result whereby

the interaction of financial frictions with elevated uncertainty is crucial towards generating the

stylized facts within the theoretical model. These findings are summarized in figures 10, 11 and

table 5.

In the next section, I discuss the welfare costs of higher financial frictions and why this in-

teraction of financial frictions and uncertainty is crucial towards generating the excess volatility

in merging countries.

Figure 10: Comparing impulse responses to a 1% uncertainty shock generated from the STVARmodel (solid line) and theoretical model (dashed line) for emerging countries - averaged acrossMexico, Chile, Argentina and South Korea

Figure 11: Comparing impulse responses to a 1% uncertainty shock generated from the STVARmodel (solid line) and theoretical model (dashed line) for the advanced economies - averagedacross the U.K., the U.S., France and Canada

43

5 Welfare implications of uncertainty and financial frictions -

which hurts more?

The transmission mechanism and results from the estimation shed light on the efficacy of the

set-up in providing a structural interpretation of the differences that characterize the interaction

of uncertainty shocks and financial frictions across advanced and emerging countries. While

these findings suggest this channel as a key factor in driving the excess volatility of real variables

in emerging countries, the set-up can also be used to understand the welfare implications.

Given that the model is solved using a third order approximation, the framework allows

me to compare the steady states with and without uncertainty to understand the magnitude of

distortions introduced by financial frictions and uncertainty respectively. In table 6, I outline

the non-stochastic and stochastic steady states for calibrations corresponding to representative

advanced (k=2.5 and ν = 0.04) and emerging countries (k=2.5 and ν = 0.07) and calibrating

average uncertainty to 0.112 respectively. The stochastic steady state can be interpreted to be

the ergodic mean of the system. It has been calculated by simulating the model 10,000 times

using k=2.5 and ν = 0.04 for advanced and k=2.5 and ν = 0.07 for emerging countries, average

uncertainty 0.112 and subsequently selecting positive shocks to uCt ,21 to compute the average

value across these simulations.

Non-Stochastic Steady State Stochastic Steady State - Ergodic MeanVariable k=2.5

& ν = 0.04(a)

k=2.5& ν = 0.07(b)

k=2.5& ν = 0.04(c)

k=2.5& ν = 0.07(d)

GDP 5.21 4.32(%∆b/a=-17%)

3.62(%∆c/a=-31%)

2.01(%∆d/c=-45%, %∆d/b=-54%)

Investment 1.36 0.93(%∆b/a=-31%)

0.82(%∆c/a=-40%)

0.18(%∆d/c=-78%, %∆d/b=-81%)

Consumption 3.26 3.08(%∆b/a=-5%)

3.32(%∆c/a=2%)

2.52(%∆d/c=-24%, %∆d/b=-18%)

Table 6: Comparing the steady state values for different values of the elasticity of borrowingcosts with respect to leverage (ν) and leverage k. The %∆y/x indicate the % change real activitybetween scenarios y and x. The results highlight the importance of the interaction betweenuncertainty and financial frictions in generating lower steady state output for representativeemrging countries in comparison to advanced countries.

Simply by changing the elasticity of borrowing costs with respect to leverage (ν) the model

21This is because the shock processes are specified in levels to prevent the volatility of σzt and σat from impactingthe average values of at and zt through a Jensen’s inequality effect.

44

can generate a lower level of real activity for the calibration corresponding to the emerging

country. I compare these outcomes as %∆b/a,%∆d/c in table 6 to outline which of the two

distortions hurt agents more in this model economy. When I consider differences in borrowing

costs only (and compare the non-stochastic steady states of the model - %∆b/a) I find that

output, consumption, and investment are about 17, 5, 31% lower in emerging countries. This

result is not surprising since financial market imperfections operate through the investment

decisions in this model. However, once I consider the role of uncertainty and carry out a

similar comparison for the stochastic steady states (%∆d/c), I find that GDP, consumption and

investment are 45, 24 and 78% lower in the representative emerging country vis-a-advanced

country. This highlights the joint importance of uncertainty and financial frictions.

The model is simple yet provides a relevant way to quantify the interaction of financial

fragility and macroeconomic uncertainty using both dynamics as well as welfare considerations.

This result is particularly relevant for policy implications as the welfare losses under uncertainty

are disproportionately larger for countries with weaker financial markets. This is captured when

I compare the reduction in real activity across the non-stochastic and stochastic steady states

across representative countries (%∆c/a - advanced countries and %∆d/b for emerging countries

respectively). Of particular relevance is the behavior of consumption. While it remains relatively

unchanged across the different steady states for the representative advanced country, steady

state consumption declines by 18% after conditioning on uncertainty for the representative

emerging country. The decrease in investment is even more sharp – 40% versus 81% for advanced

and emerging countries respectively.

The analysis of course assumes that differences in the extents of financial market development

across countries is being captured exclusively through the parameter controlling the elasticity of

borrowing costs to leverage. Nonetheless the results underscore the importance of incorporating

both fundamental features as well as characteristics of exogenous processes in understanding

the differences in real activity across advanced and emerging countries and losses in real activity

attributed to these channels.

45

6 Concluding remarks

An uncertainty shock in my open economy model with financial frictions and nominal rigidi-

ties does not impact first order properties of the model, however, manifests itself through

precautionary motives of agents in the economy to generate a decline in real activity. Even

though ex post, the higher uncertainty might not translate into negative outcomes, precau-

tionary pricing among firms and precautionary saving from households drives GDP, investment

and consumption down and triggers a recessionary scenario in the model economy. Financial

fragility, reflected in higher borrowing costs, amplifies these responses on the part of agents

for an emerging economy and in turn generates the excess volatility that distinguishes these

countries from advanced economies. This paper contributes to the existing literature by explic-

itly addressing the interaction between macroeconomic uncertainty and financial frictions and

quantifies the loss of real activity attributed to the to these two separate channels.

Although this paper does not directly address the causes of financial fragility, it takes the

differences in weaker financial institutions and infrastructure as a given and captures it through

the higher borrowing cost faced by emerging countries in international capital markets - the

results shed light on the heightened vulnerability of emerging countries to increases in aggre-

gate uncertainty. The model succeeds in matching the empirical features characterizing the

transmission of uncertainty in open economy models. From a policy perspective the framework

is particularly useful to assess changes in real activity attributed to these different channels,

either due to elevated uncertainty or elevated borrowing costs or some combination of the two.

The results suggest that investing in better integrated financial markets and robust financial

infrastructure can reduce the volatility underlying key macro variables in times of high macroe-

conomic uncertainty for emerging countries.

46

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50

Appendix

1 Pinning down E as a function of model parameters and the

steady state leverage

Given, leverage k, and capital K (from previous section) I can pin down the steady state

level of net-worth N. The steady state value of entrepreneurial capital Vt is given by:

V = [rK −Ψ(k)R∗]K + Ψ

(k)R∗N

V = [rK − kνR∗]K + kνR∗N

V = [kνR∗ − kνR∗]K + kνR∗N

V = kνR∗N = rKN

Using the equation that characterizes the evolution of net worth after accounting for fraction

(1− θ) of exiting entrepreneurs:

N = θV + (1− θ)E

N = θrKN + (1− θ)E

(1− θrK)N = (1− θ)E

D =(1− θrK)N

(1− θ)

Thus ,given N, θ, rK I can pin down the value of E that is consistent with a steady state leverage

of k. I want to point out that:

∂D

∂θ=−N(1 + rk)

(1− θ)2=⇒ ∂D

∂θ< 0

∂D

∂ν= − θN

(1− θ)+

1− θrK

1− θk∂K

∂ν,∂K

∂ν< 0 =⇒ ∂D

∂ν< 0

Thus for larger values of ν as rk increases, D decreases and may become negative. Therefore

, the calibration of θ takes into account this dynamic and ensures that D > 0

51

2 Reporting the values of γ - the parameter the governs the

smoothness of transition between regimes across countries

Country γ

US 1.6UK 1.75Canada 2.25France 2South Korea 1.75Mexico 2.5Chile 2.75Argentina 2

Table 1: Choice of γ for the sample of countries chosen in the analysis. Higher values ofγ correspond to more abrupt transitions between the recessionary and the non-recessionaryregimes. γ has been chosen to match the incidence of actual recessionary episdodes in thesample chosen for each country.

—

52

3 Data Description

Country Variable used for defining Uncertainty

U.S.(1986Q1−2014Q2)

CBOE VIX

U.K.(1979Q1−2014Q3)

FTSE Composite Index

Canada(1990Q1−2014Q4)

Composite Index Toronto Stock Exchange

South Korea(1975Q1−2014Q3)

Korea Stock Exchange - Kospi CompositeIndex

France(1991Q1−2014Q4)

Stock Market Index - SBF 250 Index

Mexico(1993Q1−2014Q2)

Mexican Stock Exchange: Bolsa IPC

Chile(1993Q1−2014Q2)

Santiago Stock Exchange- IGPA Index

Argentina(1993Q1−2014Q2)

Buenos Aires Stock Exchange - Merval In-dex

Table 2: Defining Uncertainty

53

Country GDP -Total

GrossFixedCapitalForma-tion

PrivateCon-sumptionExpendi-ture

GDP De-flator

Exportsof GoodsandServices

Importsof GoodsandServices

Interest Rate

U.S.(1986Q1− 2014Q2)

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

Effective Fed-eral FundsRate - FRED

U.K.(1979Q1− 2014Q3)

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

3-Month or 90-day Rates andYields: Trea-sury Securitiesfor the U.K. -FRED

Canada(1990Q1− 2014Q4)

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

Not Used

France(1991Q1− 2014Q4)

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

Not Used

South Korea(1975Q1− 2014Q3)

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

Not Used

Mexico(1993Q1− 2014Q2)

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

3-Month or 90-day Rates andYields: Trea-sury Securitiesfor Mexico -FRED

Chile(1993Q1− 2014Q2)

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

OECDMainEconomicIndica-tors

Not Used

Argentina(1993Q1− 2014Q2)

IMF,Interna-tionalFinancialStatistics(IFS)

IMF,Interna-tionalFinancialStatistics(IFS)

IMF,Interna-tionalFinancialStatistics(IFS)

IMF,Interna-tionalFinancialStatistics(IFS)

IMF,Interna-tionalFinancialStatistics(IFS)

IMF,Interna-tionalFinancialStatistics(IFS)

Not Used

Table 3: Data Definitions. Variables reported are seasonally adjusted and recorded in localcurrency units.

54